Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3

Percentage Accurate: 97.9% → 100.0%

Time: 5.4s

Alternatives: 7

Speedup: 1.3×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot y + \left(1 - x\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) + ((1.0d0 - x) * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

Python

def code(x, y, z):
	return (x * y) + ((1.0 - x) * z)

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + ((1.0 - x) * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y + \left(1 - x\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) + ((1.0d0 - x) * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

Python

def code(x, y, z):
	return (x * y) + ((1.0 - x) * z)

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + ((1.0 - x) * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ z + x \cdot \left(y - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (* x (- y z))))

C

double code(double x, double y, double z) {
	return z + (x * (y - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z + (x * (y - z))
end function

Java

public static double code(double x, double y, double z) {
	return z + (x * (y - z));
}

Python

def code(x, y, z):
	return z + (x * (y - z))

Julia

function code(x, y, z)
	return Float64(z + Float64(x * Float64(y - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + (x * (y - z));
end

Wolfram

code[x_, y_, z_] := N[(z + N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[x \cdot y + \left(1 - x\right) \cdot z \]
2. Step-by-step derivation

   1. +-commutative 98.8%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot z + x \cdot y} \]

   2. *-commutative 98.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - x\right)} + x \cdot y \]

   3. sub-neg 98.8%

      \[\leadsto z \cdot \color{blue}{\left(1 + \left(-x\right)\right)} + x \cdot y \]

   4. distribute-lft-in 98.8%

      \[\leadsto \color{blue}{\left(z \cdot 1 + z \cdot \left(-x\right)\right)} + x \cdot y \]

   5. associate-+l+ 98.8%

      \[\leadsto \color{blue}{z \cdot 1 + \left(z \cdot \left(-x\right) + x \cdot y\right)} \]

   6. *-rgt-identity 98.8%

      \[\leadsto \color{blue}{z} + \left(z \cdot \left(-x\right) + x \cdot y\right) \]

   7. cancel-sign-sub 98.8%

      \[\leadsto z + \color{blue}{\left(z \cdot \left(-x\right) - \left(-x\right) \cdot y\right)} \]

   8. *-commutative 98.8%

      \[\leadsto z + \left(z \cdot \left(-x\right) - \color{blue}{y \cdot \left(-x\right)}\right) \]

   9. cancel-sign-sub-inv 98.8%

      \[\leadsto z + \color{blue}{\left(z \cdot \left(-x\right) + \left(-y\right) \cdot \left(-x\right)\right)} \]

   10. distribute-rgt-out 100.0%

       \[\leadsto z + \color{blue}{\left(-x\right) \cdot \left(z + \left(-y\right)\right)} \]

   11. cancel-sign-sub-inv 100.0%

       \[\leadsto \color{blue}{z - x \cdot \left(z + \left(-y\right)\right)} \]

   12. distribute-lft-out 98.8%

       \[\leadsto z - \color{blue}{\left(x \cdot z + x \cdot \left(-y\right)\right)} \]

   13. distribute-rgt-neg-out 98.8%

       \[\leadsto z - \left(x \cdot z + \color{blue}{\left(-x \cdot y\right)}\right) \]

   14. sub-neg 98.8%

       \[\leadsto z - \color{blue}{\left(x \cdot z - x \cdot y\right)} \]

   15. distribute-lft-out-- 100.0%

       \[\leadsto z - \color{blue}{x \cdot \left(z - y\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{z - x \cdot \left(z - y\right)} \]

4. Final simplification 100.0%

   \[\leadsto z + x \cdot \left(y - z\right) \]

Alternative 2: 58.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+232}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+53}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-159}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-50}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+131} \lor \neg \left(x \leq 10^{+159}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= x -2.3e+232)
     (* x y)
     (if (<= x -2.7e+147)
       t_0
       (if (<= x -4.6e+53)
         (* x y)
         (if (<= x -1.0)
           t_0
           (if (<= x 7e-159)
             z
             (if (<= x 7.6e-50)
               (* x y)
               (if (<= x 1.0)
                 z
                 (if (or (<= x 6e+131) (not (<= x 1e+159)))
                   t_0
                   (* x y)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -2.3e+232) {
		tmp = x * y;
	} else if (x <= -2.7e+147) {
		tmp = t_0;
	} else if (x <= -4.6e+53) {
		tmp = x * y;
	} else if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 7e-159) {
		tmp = z;
	} else if (x <= 7.6e-50) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = z;
	} else if ((x <= 6e+131) || !(x <= 1e+159)) {
		tmp = t_0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (x <= (-2.3d+232)) then
        tmp = x * y
    else if (x <= (-2.7d+147)) then
        tmp = t_0
    else if (x <= (-4.6d+53)) then
        tmp = x * y
    else if (x <= (-1.0d0)) then
        tmp = t_0
    else if (x <= 7d-159) then
        tmp = z
    else if (x <= 7.6d-50) then
        tmp = x * y
    else if (x <= 1.0d0) then
        tmp = z
    else if ((x <= 6d+131) .or. (.not. (x <= 1d+159))) then
        tmp = t_0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -2.3e+232) {
		tmp = x * y;
	} else if (x <= -2.7e+147) {
		tmp = t_0;
	} else if (x <= -4.6e+53) {
		tmp = x * y;
	} else if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 7e-159) {
		tmp = z;
	} else if (x <= 7.6e-50) {
		tmp = x * y;
	} else if (x <= 1.0) {
		tmp = z;
	} else if ((x <= 6e+131) || !(x <= 1e+159)) {
		tmp = t_0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if x <= -2.3e+232:
		tmp = x * y
	elif x <= -2.7e+147:
		tmp = t_0
	elif x <= -4.6e+53:
		tmp = x * y
	elif x <= -1.0:
		tmp = t_0
	elif x <= 7e-159:
		tmp = z
	elif x <= 7.6e-50:
		tmp = x * y
	elif x <= 1.0:
		tmp = z
	elif (x <= 6e+131) or not (x <= 1e+159):
		tmp = t_0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (x <= -2.3e+232)
		tmp = Float64(x * y);
	elseif (x <= -2.7e+147)
		tmp = t_0;
	elseif (x <= -4.6e+53)
		tmp = Float64(x * y);
	elseif (x <= -1.0)
		tmp = t_0;
	elseif (x <= 7e-159)
		tmp = z;
	elseif (x <= 7.6e-50)
		tmp = Float64(x * y);
	elseif (x <= 1.0)
		tmp = z;
	elseif ((x <= 6e+131) || !(x <= 1e+159))
		tmp = t_0;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (x <= -2.3e+232)
		tmp = x * y;
	elseif (x <= -2.7e+147)
		tmp = t_0;
	elseif (x <= -4.6e+53)
		tmp = x * y;
	elseif (x <= -1.0)
		tmp = t_0;
	elseif (x <= 7e-159)
		tmp = z;
	elseif (x <= 7.6e-50)
		tmp = x * y;
	elseif (x <= 1.0)
		tmp = z;
	elseif ((x <= 6e+131) || ~((x <= 1e+159)))
		tmp = t_0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[x, -2.3e+232], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.7e+147], t$95$0, If[LessEqual[x, -4.6e+53], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, 7e-159], z, If[LessEqual[x, 7.6e-50], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.0], z, If[Or[LessEqual[x, 6e+131], N[Not[LessEqual[x, 1e+159]], $MachinePrecision]], t$95$0, N[(x * y), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.30000000000000006e232 or -2.69999999999999998e147 < x < -4.60000000000000039e53 or 7.00000000000000005e-159 < x < 7.5999999999999998e-50 or 6.0000000000000003e131 < x < 9.9999999999999993e158

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around inf 71.4%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -2.30000000000000006e232 < x < -2.69999999999999998e147 or -4.60000000000000039e53 < x < -1 or 1 < x < 6.0000000000000003e131 or 9.9999999999999993e158 < x

   1. Initial program 96.8%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 97.9%

      \[\leadsto \color{blue}{x \cdot \left(y + -1 \cdot z\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 97.9%

         \[\leadsto x \cdot \left(y + \color{blue}{\left(-z\right)}\right) \]

      2. sub-neg 97.9%

         \[\leadsto x \cdot \color{blue}{\left(y - z\right)} \]

   4. Simplified 97.9%

      \[\leadsto \color{blue}{x \cdot \left(y - z\right)} \]

   5. Taylor expanded in y around 0 68.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot z\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 68.1%

         \[\leadsto \color{blue}{-x \cdot z} \]

      2. distribute-lft-neg-in 68.1%

         \[\leadsto \color{blue}{\left(-x\right) \cdot z} \]

      3. *-commutative 68.1%

         \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   7. Simplified 68.1%

      \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   if -1 < x < 7.00000000000000005e-159 or 7.5999999999999998e-50 < x < 1

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 72.2%

      \[\leadsto \color{blue}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+232}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+53}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-159}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-50}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+131} \lor \neg \left(x \leq 10^{+159}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 82.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-160}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y z))))
   (if (<= x -1.45e-57)
     t_0
     (if (<= x 7.2e-160)
       z
       (if (<= x 7e-49) (* x y) (if (<= x 3.2e-7) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (x <= -1.45e-57) {
		tmp = t_0;
	} else if (x <= 7.2e-160) {
		tmp = z;
	} else if (x <= 7e-49) {
		tmp = x * y;
	} else if (x <= 3.2e-7) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y - z)
    if (x <= (-1.45d-57)) then
        tmp = t_0
    else if (x <= 7.2d-160) then
        tmp = z
    else if (x <= 7d-49) then
        tmp = x * y
    else if (x <= 3.2d-7) then
        tmp = z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (x <= -1.45e-57) {
		tmp = t_0;
	} else if (x <= 7.2e-160) {
		tmp = z;
	} else if (x <= 7e-49) {
		tmp = x * y;
	} else if (x <= 3.2e-7) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y - z)
	tmp = 0
	if x <= -1.45e-57:
		tmp = t_0
	elif x <= 7.2e-160:
		tmp = z
	elif x <= 7e-49:
		tmp = x * y
	elif x <= 3.2e-7:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y - z))
	tmp = 0.0
	if (x <= -1.45e-57)
		tmp = t_0;
	elseif (x <= 7.2e-160)
		tmp = z;
	elseif (x <= 7e-49)
		tmp = Float64(x * y);
	elseif (x <= 3.2e-7)
		tmp = z;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y - z);
	tmp = 0.0;
	if (x <= -1.45e-57)
		tmp = t_0;
	elseif (x <= 7.2e-160)
		tmp = z;
	elseif (x <= 7e-49)
		tmp = x * y;
	elseif (x <= 3.2e-7)
		tmp = z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e-57], t$95$0, If[LessEqual[x, 7.2e-160], z, If[LessEqual[x, 7e-49], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.2e-7], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45000000000000013e-57 or 3.2000000000000001e-7 < x

   1. Initial program 97.9%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 96.2%

      \[\leadsto \color{blue}{x \cdot \left(y + -1 \cdot z\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 96.2%

         \[\leadsto x \cdot \left(y + \color{blue}{\left(-z\right)}\right) \]

      2. sub-neg 96.2%

         \[\leadsto x \cdot \color{blue}{\left(y - z\right)} \]

   4. Simplified 96.2%

      \[\leadsto \color{blue}{x \cdot \left(y - z\right)} \]

   if -1.45000000000000013e-57 < x < 7.1999999999999994e-160 or 7.00000000000000012e-49 < x < 3.2000000000000001e-7

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 77.9%

      \[\leadsto \color{blue}{z} \]

   if 7.1999999999999994e-160 < x < 7.00000000000000012e-49

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around inf 61.0%

      \[\leadsto \color{blue}{x \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-160}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]

Alternative 4: 59.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-54} \lor \neg \left(x \leq 7 \cdot 10^{-159}\right) \land \left(x \leq 8.5 \cdot 10^{-50} \lor \neg \left(x \leq 6.4 \cdot 10^{-9}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.8e-54)
         (and (not (<= x 7e-159)) (or (<= x 8.5e-50) (not (<= x 6.4e-9)))))
   (* x y)
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e-54) || (!(x <= 7e-159) && ((x <= 8.5e-50) || !(x <= 6.4e-9)))) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-6.8d-54)) .or. (.not. (x <= 7d-159)) .and. (x <= 8.5d-50) .or. (.not. (x <= 6.4d-9))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e-54) || (!(x <= 7e-159) && ((x <= 8.5e-50) || !(x <= 6.4e-9)))) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.8e-54) or (not (x <= 7e-159) and ((x <= 8.5e-50) or not (x <= 6.4e-9))):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.8e-54) || (!(x <= 7e-159) && ((x <= 8.5e-50) || !(x <= 6.4e-9))))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.8e-54) || (~((x <= 7e-159)) && ((x <= 8.5e-50) || ~((x <= 6.4e-9)))))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.8e-54], And[N[Not[LessEqual[x, 7e-159]], $MachinePrecision], Or[LessEqual[x, 8.5e-50], N[Not[LessEqual[x, 6.4e-9]], $MachinePrecision]]]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -6.79999999999999975e-54 or 7.00000000000000005e-159 < x < 8.50000000000000012e-50 or 6.40000000000000023e-9 < x

   1. Initial program 98.3%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in y around inf 50.2%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -6.79999999999999975e-54 < x < 7.00000000000000005e-159 or 8.50000000000000012e-50 < x < 6.40000000000000023e-9

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around 0 77.9%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-54} \lor \neg \left(x \leq 7 \cdot 10^{-159}\right) \land \left(x \leq 8.5 \cdot 10^{-50} \lor \neg \left(x \leq 6.4 \cdot 10^{-9}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-15} \lor \neg \left(z \leq 5.4 \cdot 10^{+29}\right):\\ \;\;\;\;z - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e-15) (not (<= z 5.4e+29))) (- z (* z x)) (* x (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-15) || !(z <= 5.4e+29)) {
		tmp = z - (z * x);
	} else {
		tmp = x * (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3d-15)) .or. (.not. (z <= 5.4d+29))) then
        tmp = z - (z * x)
    else
        tmp = x * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-15) || !(z <= 5.4e+29)) {
		tmp = z - (z * x);
	} else {
		tmp = x * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e-15) or not (z <= 5.4e+29):
		tmp = z - (z * x)
	else:
		tmp = x * (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e-15) || !(z <= 5.4e+29))
		tmp = Float64(z - Float64(z * x));
	else
		tmp = Float64(x * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3e-15) || ~((z <= 5.4e+29)))
		tmp = z - (z * x);
	else
		tmp = x * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e-15], N[Not[LessEqual[z, 5.4e+29]], $MachinePrecision]], N[(z - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e-15 or 5.4e29 < z

   1. Initial program 97.4%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 97.4%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot z + x \cdot y} \]

      2. *-commutative 97.4%

         \[\leadsto \color{blue}{z \cdot \left(1 - x\right)} + x \cdot y \]

      3. sub-neg 97.4%

         \[\leadsto z \cdot \color{blue}{\left(1 + \left(-x\right)\right)} + x \cdot y \]

      4. distribute-lft-in 97.4%

         \[\leadsto \color{blue}{\left(z \cdot 1 + z \cdot \left(-x\right)\right)} + x \cdot y \]

      5. associate-+l+ 97.4%

         \[\leadsto \color{blue}{z \cdot 1 + \left(z \cdot \left(-x\right) + x \cdot y\right)} \]

      6. *-rgt-identity 97.4%

         \[\leadsto \color{blue}{z} + \left(z \cdot \left(-x\right) + x \cdot y\right) \]

      7. cancel-sign-sub 97.4%

         \[\leadsto z + \color{blue}{\left(z \cdot \left(-x\right) - \left(-x\right) \cdot y\right)} \]

      8. *-commutative 97.4%

         \[\leadsto z + \left(z \cdot \left(-x\right) - \color{blue}{y \cdot \left(-x\right)}\right) \]

      9. cancel-sign-sub-inv 97.4%

         \[\leadsto z + \color{blue}{\left(z \cdot \left(-x\right) + \left(-y\right) \cdot \left(-x\right)\right)} \]

      10. distribute-rgt-out 100.0%

          \[\leadsto z + \color{blue}{\left(-x\right) \cdot \left(z + \left(-y\right)\right)} \]

      11. cancel-sign-sub-inv 100.0%

          \[\leadsto \color{blue}{z - x \cdot \left(z + \left(-y\right)\right)} \]

      12. distribute-lft-out 97.4%

          \[\leadsto z - \color{blue}{\left(x \cdot z + x \cdot \left(-y\right)\right)} \]

      13. distribute-rgt-neg-out 97.4%

          \[\leadsto z - \left(x \cdot z + \color{blue}{\left(-x \cdot y\right)}\right) \]

      14. sub-neg 97.4%

          \[\leadsto z - \color{blue}{\left(x \cdot z - x \cdot y\right)} \]

      15. distribute-lft-out-- 100.0%

          \[\leadsto z - \color{blue}{x \cdot \left(z - y\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z - x \cdot \left(z - y\right)} \]

   4. Taylor expanded in z around inf 88.8%

      \[\leadsto z - \color{blue}{x \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 88.8%

         \[\leadsto z - \color{blue}{z \cdot x} \]

   6. Simplified 88.8%

      \[\leadsto z - \color{blue}{z \cdot x} \]

   if -3e-15 < z < 5.4e29

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 80.9%

      \[\leadsto \color{blue}{x \cdot \left(y + -1 \cdot z\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 80.9%

         \[\leadsto x \cdot \left(y + \color{blue}{\left(-z\right)}\right) \]

      2. sub-neg 80.9%

         \[\leadsto x \cdot \color{blue}{\left(y - z\right)} \]

   4. Simplified 80.9%

      \[\leadsto \color{blue}{x \cdot \left(y - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-15} \lor \neg \left(z \leq 5.4 \cdot 10^{+29}\right):\\ \;\;\;\;z - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]

Alternative 6: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.4 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.4e-6))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.4e-6)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.4d-6))) then
        tmp = x * (y - z)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.4e-6)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.4e-6):
		tmp = x * (y - z)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.4e-6))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.4e-6)))
		tmp = x * (y - z);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.4e-6]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.39999999999999994e-6 < x

   1. Initial program 97.8%

      \[x \cdot y + \left(1 - x\right) \cdot z \]

   2. Taylor expanded in x around inf 98.5%

      \[\leadsto \color{blue}{x \cdot \left(y + -1 \cdot z\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 98.5%

         \[\leadsto x \cdot \left(y + \color{blue}{\left(-z\right)}\right) \]

      2. sub-neg 98.5%

         \[\leadsto x \cdot \color{blue}{\left(y - z\right)} \]

   4. Simplified 98.5%

      \[\leadsto \color{blue}{x \cdot \left(y - z\right)} \]

   if -1 < x < 1.39999999999999994e-6

   1. Initial program 100.0%

      \[x \cdot y + \left(1 - x\right) \cdot z \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot z + x \cdot y} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{z \cdot \left(1 - x\right)} + x \cdot y \]

      3. sub-neg 100.0%

         \[\leadsto z \cdot \color{blue}{\left(1 + \left(-x\right)\right)} + x \cdot y \]

      4. distribute-lft-in 100.0%

         \[\leadsto \color{blue}{\left(z \cdot 1 + z \cdot \left(-x\right)\right)} + x \cdot y \]

      5. associate-+l+ 100.0%

         \[\leadsto \color{blue}{z \cdot 1 + \left(z \cdot \left(-x\right) + x \cdot y\right)} \]

      6. *-rgt-identity 100.0%

         \[\leadsto \color{blue}{z} + \left(z \cdot \left(-x\right) + x \cdot y\right) \]

      7. cancel-sign-sub 100.0%

         \[\leadsto z + \color{blue}{\left(z \cdot \left(-x\right) - \left(-x\right) \cdot y\right)} \]

      8. *-commutative 100.0%

         \[\leadsto z + \left(z \cdot \left(-x\right) - \color{blue}{y \cdot \left(-x\right)}\right) \]

      9. cancel-sign-sub-inv 100.0%

         \[\leadsto z + \color{blue}{\left(z \cdot \left(-x\right) + \left(-y\right) \cdot \left(-x\right)\right)} \]

      10. distribute-rgt-out 100.0%

          \[\leadsto z + \color{blue}{\left(-x\right) \cdot \left(z + \left(-y\right)\right)} \]

      11. cancel-sign-sub-inv 100.0%

          \[\leadsto \color{blue}{z - x \cdot \left(z + \left(-y\right)\right)} \]

      12. distribute-lft-out 100.0%

          \[\leadsto z - \color{blue}{\left(x \cdot z + x \cdot \left(-y\right)\right)} \]

      13. distribute-rgt-neg-out 100.0%

          \[\leadsto z - \left(x \cdot z + \color{blue}{\left(-x \cdot y\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto z - \color{blue}{\left(x \cdot z - x \cdot y\right)} \]

      15. distribute-lft-out-- 100.0%

          \[\leadsto z - \color{blue}{x \cdot \left(z - y\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z - x \cdot \left(z - y\right)} \]

   4. Taylor expanded in z around 0 98.4%

      \[\leadsto z - \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 98.4%

         \[\leadsto z - \color{blue}{\left(-x \cdot y\right)} \]

      2. distribute-rgt-neg-out 98.4%

         \[\leadsto z - \color{blue}{x \cdot \left(-y\right)} \]

   6. Simplified 98.4%

      \[\leadsto z - \color{blue}{x \cdot \left(-y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.4 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 7: 37.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

double code(double x, double y, double z) {
	return z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

public static double code(double x, double y, double z) {
	return z;
}

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

function tmp = code(x, y, z)
	tmp = z;
end

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 98.8%

   \[x \cdot y + \left(1 - x\right) \cdot z \]

2. Taylor expanded in x around 0 31.2%

   \[\leadsto \color{blue}{z} \]

3. Final simplification 31.2%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023326 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))